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MathGroup Archive 2001

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Re: Simplifying expressions, and Alpha

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31352] Re: [mg31336] Simplifying expressions, and Alpha
  • From: BobHanlon at aol.com
  • Date: Tue, 30 Oct 2001 04:35:36 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/10/29 2:53:24 AM, msdawy at hotmail.com writes:

>i have 2 problems... i'd be very grateful if anyone could help me..
>1. some expressions return very complex expressions (e.g. when u solve
>a third degree equation), you get a very complex formula for the
>result. i am looking for a way to output the result in a
>human-readable format (like 2.3342218) not with many roots, and stuff
>like this, how can i do it?
>
>2. how can i find the point on a chi squared distribution where the
>CDF will be 0.995?
>

1.  Use N[Solve[]], Solve[]//N, or just NSolve[].

2.  The inverse of CDF is Quantile.

Needs["Statistics`ContinuousDistributions`"];

Quantile[ChiSquareDistribution[n], x]

2*InverseGammaRegularized[n/2, 0, x]

Quantile[ChiSquareDistribution[3], 0.995]

12.838156466598651

or using Solve

Solve[CDF[ChiSquareDistribution[n], q] == x, q]

{{q -> 2*InverseGammaRegularized[
      n/2, 0, x]}}

Solve[CDF[ChiSquareDistribution[3], q] == 0.995, q]

{{q -> 12.838156466598651}}

Plot[Evaluate[Table[
        CDF[ChiSquareDistribution[n], x], 
        {n, 1, 5, 2}]], {x, 0, 20}, 
    PlotStyle -> Table[Hue[k/3], {k, 0, 2}], 
    AspectRatio -> 1];

Plot[Evaluate[Table[
        Quantile[ChiSquareDistribution[n], x], 
        {n, 1, 5, 2}]], {x, 0, 1}, 
    PlotStyle -> Table[Hue[k/3], {k, 0, 2}], 
    PlotRange -> {0, 20.5}, AspectRatio -> 1];


Bob Hanlon
Chantilly, VA  USA


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